Why Do The Latest Sunrises Occur After The Winter Solstice?

We all know that the winter solstice has the shortest daylight of the year. But you might be surprised to learn that this solstice has neither the earliest sunset, nor the latest sunrise, of any day throughout the year. This past year, Portland’s earliest sunset occurred on December 10, while Portland’s latest sunrise occurred on January 1, 2021. How can this be?

In order to understand this “offset” in timing between sunrises and sunsets around the solstice, we first need to understand the concept of a “solar day” and how it differs from the standard 24-hour day we use in everyday life. A solar day is defined as the time between successive “solar noons,” or the exact time at which the sun is at its highest point in the sky. The solar day varies from approximately 24 hours and 30 seconds near Christmas Day to 23 hours, 59 minutes, and 38 seconds in mid-September. These differences in the length of the solar day can cause the solar noon to vary from its average value by as much as 15 minutes over the course of the year.

There are two reasons why the length of the solar day varies throughout the year. The first is that the Earth’s orbit around the sun is not a perfect circle but is instead an ellipse, with the Earth being three million miles closer to the sun in January than July. When the Earth is closer to the sun, it orbits at a slightly faster rate, and this makes the solar day slightly longer, as the Earth must make an additional fraction of a rotation to reach solar noon. During July, when the Earth is farther away, it orbits at a slower rate, and this makes the solar day slightly shorter. The points at which the Earth is the furthest from and closest to the sun are called perihelion and aphelion, respectively.

Note that the Earth spins on its axis once every 23 hours and 56 minutes, not once every 24 hours – the extra 4 minutes in our day are needed to complete a solar day because the Earth is orbiting the sun and thus has to make slightly more than one full rotation each day to reach solar noon.

The second reason why the length of the solar day varies throughout the year is due to the Earth’s axial tilt. This effect is a bit harder to illustrate – we are familiar with how the Earth’s axial tilt causes our seasons, but it might not be immediately apparent how it can make our actual days longer or shorter. To understand how the axial tilt and length of day are related, it’s useful to view the sun inclined relative to the Earth, like in the image below.

In the equinoxes, when the sun is directly over the equator, the sun has a lot of north/south movement but relatively little east-west (parallel to the equator) movement. Meanwhile, at the solstices, when the sun is highest or lowest in the sky, the reverse is true – the sun is primarily moving east/west in the sky, with relatively little north/south movement. The speed of the sun’s apparent east-west movement is what determines the length of the solar day – when the sun is moving east-west at a slower rate (as it does during the equinoxes, the Earth doesn’t need to rotate as much to “keep up” with the sun’s east-west progression, and the solar day is shortened. Near the solstices, when the sun is moving east/west at a faster rate, the solar day is longer, as the Earth needs more time to “catch up” with the east/west movement of the sun.

This means that during the spring (autumn) equinox, the sun is rising (falling) rapidly in the sky and the length of daylight is increasing (decreasing) at the highest rate of the year, but to compensate for this, the sun appears to be orbiting the Earth at a slower rate, and the solar day is shortened. Near the winter and summer solstices, the reverse is true; the length of daylight isn’t changing much, but the sun appears to orbit the earth more quickly, and the solar day is lengthened.

Putting these two effects together, we get something called the “equation of time,” which shows how ahead/behind a sundial is compared to mean solar time throughout the year. When the slope of the curve is going down, days are becoming longer and solar noon is trending later (since consecutive solar noons are greater than 24 hours apart), and when the slope is going up, days are becoming shorter and solar noon is trending earlier (since consecutive solar noons are less than 24 hours apart).

One way to track how the timing the solar day varies throughout the year is by using an analemma. An analemma is a diagram that shows the position of the sun at a fixed time over the course of a year. We are familiar with how the sun’s altitude changes at solar noon throughout the year – it is lower on the horizon in the winter than the summer. An analemma allows us to more clearly see the sun’s east/west movement  by tracking how solar noon varies throughout the year. For example, if an analemma was taken and the time of the photograph was mean solar noon, we would be able to see that solar noon occurred “early” in the autumn and “late” in the winter.

You can get a rough estimate of how much solar noon varies throughout the year by seeing how “wide” the analemma is. According to this nifty calculator, the earliest solar noon of 2021 for Portland will be November 2nd, while the latest will be February 10, with the February 10 solar noon being about 30 minutes later than the one on November 2nd.

Putting all this together, the reason why our earliest sunsets and latest sunrises are nearly a month apart is because solar noon becomes progressively later over the month of December. Thankfully, our sunrises and sunsets are trending earlier and later now, respectively, and in just a few weeks we should start to see the first winter crocuses emerge – a sign that spring is not as far away as it may seem.